Depth of the 3-path Ideal of Square of a Path

In this note, we compute depth of the 3-path ideal of square of a path and show that the 3-path ideal I3(P 2 n) of square of a path graph is Cohen-Macaulay if and only if n = 3 or 4. Also, we consider the limit behavior of depth of powers of the 3-path ideal of square of a path.

Publication Details

Journal
ArXiv.org
Published
2025-07-11
Primary Topic
Technology in Education and Healthcare
Type
article
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article

Depth of the 3-path Ideal of Square of a Path

ArXiv.org
Technology in Education and Healthcare
article

Depth of the 3-path Ideal of Square of a Path

article en

Abstract

In this note, we compute depth of the 3-path ideal of square of a path and show that the 3-path ideal I3(P 2 n) of square of a path graph is Cohen-Macaulay if and only if n = 3 or 4. Also, we consider the limit behavior of depth of powers of the 3-path ideal of square of a path.

ArXiv.org
Openalex Percentile: Top 38%
Technology in Education and Healthcare
Open Access PDFOpenAlex
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Depth of the 3-path Ideal of Square of a Path · ArXiv.org (2025) | TGRS Research Map | TGRS